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PAC-Bayes-Chernoff bounds for unbounded losses 24

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PAC-Bayes-Chernoff bounds for unbounded losses

Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Ioar Casado Luis A. Ortega Aritz Pérez Andrés R. Masegosa Machine Learning Group Basque Center for Applied Mathematics (BCAM) Machine Learning Group Computer Science Dept. - EPS. Universidad Autónoma de Madrid Department of Computer Science Aalborg University

ISBN: (纸本)9798331314385

We introduce a new PAC-Bayes oracle bound for unbounded losses that extends Cramér-Chernoff bounds to the PAC-Bayesian setting. The proof technique relies on controlling the tails of certain random variables involving the Cramér transform of the loss. Our approach naturally leverages properties of Cramér-Chernoff bounds, such as exact optimization of the free parameter in many PAC-Bayes bounds. We highlight several applications of the main theorem. Firstly, we show that our bound recovers and generalizes previous results. Additionally, our approach allows working with richer assumptions that result in more informative and potentially tighter bounds. In this direction, we provide a general bound under a new model-dependent assumption from which we obtain bounds based on parameter norms and log-Sobolev inequalities. Notably, many of these bounds can be minimized to obtain distributions beyond the Gibbs posterior and provide novel theoretical coverage to existing regularization techniques.

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A General Identification Algorithm For Data Fusion Problems Under Systematic Selection

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arXiv 2024年

作者： Lee, Jaron J.R. Ghassami, AmirEmad Shpitser, Ilya Department of Computer Science Johns Hopkins University BaltimoreMD United States Department of Applied Mathematics and Statistics Boston University BostonMA United States

Causal inference is made challenging by confounding, selection bias, and other complications. A common approach to addressing these difficulties is the inclusion of auxiliary data on the superpopulation of interest. Such data may measure a different set of variables, or be obtained under different experimental conditions than the primary dataset. Analysis based on multiple datasets must carefully account for similarities between datasets, while appropriately accounting for differences. In addition, selection of experimental units into different datasets may be systematic;similar difficulties are encountered in missing data problems. Existing methods for combining datasets either do not consider this issue, or assume simple selection mechanisms. In this paper, we provide a general approach, based on graphical causal models, for causal inference from data on the same superpopulation that is obtained under different experimental conditions. Our framework allows both arbitrary unobserved confounding, and arbitrary selection processes into different experimental regimes in our data. We describe how systematic selection processes may be organized into a hierarchy similar to censoring processes in missing data: selected completely at random (SCAR), selected at random (SAR), and selected not at random (SNAR). In addition, we provide a general identification algorithm for interventional distributions in this setting. Copyright © 2024, The Authors. All rights reserved.

关键词： Data fusion

Cooling Yb-Doped Silica Fibers and Fiber Lasers with Anti-Stokes Pumping 5

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Cooling Yb-Doped Silica Fibers and Fiber Lasers with Anti-St...

Photonic Heat Engines: science and Applications V 2023

作者： Frey, Benjamin N. Balliu, Enkeleda Vigneron, Pierre-Baptiste Knall, Jenny Hawkins, Thomas W. Meehan, Bailey Cahoon, Mary Ann Ballato, John Engholm, Magnus Dragic, Peter D. Yu, Nanjie Boilard, Tommy Bernier, Martin Digonnet, Michel J.F. Applied Physics Department Stanford University CA United States Department of Engineering Mathematics and Science Education Mid Sweden University Sundsvall Sweden Department of Materials Science and Engineering Clemson University South Carolina United States Department of Electrical Computer Engineering U. of Illinois at Urbana-Champaign IL United States Université Laval Québec Canada

ISBN: (纸本)9781510659797

Optical cooling in Yb-doped silica fibers using anti-Stokes fluorescence has become a subject of great interest in the fiber laser community. This paper provides an update on the development of silica fibers designed specifically to enhance their cooling properties. This growing list includes a new, nearly single-mode fiber with a borophosphosilicate core that produced –65 mK of cooling with only 260 mW of 1040-nm pump power. The silica compositions that have now been successfully cooled at atmospheric pressure by anti-Stokes fluorescence by our team include aluminosilicate, aluminofluorosilicate, borophosphosilicate, and aluminosilicate doped with one of three different alkali-earth nanoparticles (Ba, Sr, and Ca). By fitting the measured temperature dependence of the cooled fiber on pump power, two key parameters that control the degree of cooling are inferred, namely the critical quenching concentration and the absorptive loss due to impurities. The inferred values compiled for the fibers that cooled indicate that the extracted heat is highest when the Yb concentration is 2 wt.% or more (to maximize heat extraction), the Al concentration is ~0.8 wt.% or greater (to reduce quenching), and the absorptive loss is below approximately 15 dB/km, and ideally below 5 dB/km (to minimize heating due to pump absorption). Only two of the reported fibers, an LaF3-doped and an LuF3-doped nanoparticle fiber, did not cool, because their Yb and Al concentrations were not sufficiently high. This analysis shows that through careful composition control (especially the Al and Yb concentrations) and minimization of the OH contamination, a new generation of Yb-doped silica fibers is emerging with higher Yb concentrations, greater resistance to quenching, and lower residual loss than commercial Yb-doped fibers. They can be expected to have a significant impact not only on optically cooled devices but also on a much broader range of fiber lasers and amplifiers. © 2023 SPIE.

关键词： Nanoparticles

Depth Separation in Norm-Bounded Infinite-Width Neural Networks

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arXiv 2024年

作者： Parkinson, Suzanna Ongie, Greg Willett, Rebecca Shamir, Ohad Srebro, Nathan Committee on Computational and Applied Mathematics University of Chicago ChicagoIL United States Department of Mathematical and Statistical Sciences Marquette University MilwaukeeWI United States Department of Statistics Department of Computer Science University of Chicago ChicagoIL United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Toyota Technological Institute at Chicago ChicagoIL United States

We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared 2-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results focused on separation in terms of width, such results do not give insight into whether depth determines if it is possible to learn a network that generalizes well even when the network width is unbounded. Here, we study separation in terms of the sample complexity required for learnability. Specifically, we show that there are functions that are learnable with sample complexity polynomial in the input dimension by norm-controlled depth-3 ReLU networks, yet are not learnable with sub-exponential sample complexity by norm-controlled depth-2 ReLU networks (with any value for the norm). We also show that a similar statement in the reverse direction is not possible: any function learnable with polynomial sample complexity by a norm-controlled depth-2 ReLU network with infinite width is also learnable with polynomial sample complexity by a norm-controlled depth-3 ReLU network. © 2024, CC BY.

关键词： Polynomials

RENT DIVISION WITH PICKY ROOMMATES

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arXiv 2024年

作者： Huang, Yanqing Kitch, Madeline Melas-Kyriazi, Natalie Department of Computer Science Harvard University CambridgeMA02138 United States Department of Applied Mathematics Harvard University CambridgeMA02138 United States

How can one assign roommates and rooms when tenants have preferences for both where and with whom they live? In this setting, the usual notions of envy-freeness and maximizing social welfare may not hold;the roommate rent-division problem is assumed to be NP-hard, and even when welfare is maximized, an envy-free price vector may not exist. We first construct a novel greedy algorithm with bipartite matching before exploiting the connection between social welfare maximization and the maximum weighted independent set (MWIS) problem to construct a polynomial-time algorithm that gives a 3/4 + ϵ-approximation of maximum social welfare. Further, we present an integer program to find a room envy-free price vector that minimizes envy between any two tenants. We show empirically that a MWIS algorithm returns the optimal allocation in polynomial time and conjecture that this problem, at the forefront of computer science research, may have an exact polynomial algorithm solution. This study not only advances the theoretical framework for roommate rent division but also offers practical algorithmic solutions that can be implemented in real-world applications. Copyright © 2024, The Authors. All rights reserved.

关键词： Game theory

Segment Intersection Representations, Level Planarity and Constrained Ordering Problems

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arXiv 2025年

作者： Fink, Simon D. Pfretzschner, Matthias Stumpf, Peter Algorithms and Complexity Group Technische Universität Wien Austria Faculty of Computer Science and Mathematics University of Passau Germany Department of Theoretical Computer Science Faculty of Information Technology Czech Technical University Prague Czech Republic Department of Applied Mathematics Charles University Prague Czech Republic

In the Segment Intersection Graph Representation Problem, we want to represent the vertices of a graph as straight line segments in the plane such that two segments cross if and only if there is an edge between the corresponding vertices. This problem is NP-hard (even ∃R-complete [19]) in the general case [13] and remains so if we restrict the segments to be axis-aligned, i.e., horizontal and vertical [12]. A long standing open question for the latter variant is its complexity when the order of segments along one axis (say the vertical order of horizontal segments) is already given [12,14]. We resolve this question by giving efficient solutions using two very different approaches that are interesting on their own. First, using a graph-drawing perspective, we relate the problem to a variant of the well-known Level Planarity problem, where vertices have to lie on preassigned horizontal levels. In our case, each level also carries consecutivity constraints on its vertices;this Level Planarity variant is known to have a quadratic solution. Second, we use an entirely combinatorial approach and show that both problems can equivalently be formulated as a linear ordering problem subject to certain consecutivity constraints. While the complexity of such problems varies greatly, we show that in this case the constraints are well-structured in a way that allows a direct quadratic solution. Thus, we obtain three different-but-equivalent perspectives on this problem: the initial geometric one, one from planar graph drawing and a purely combinatorial one. © 2025, CC BY.

关键词： Graph theory

Episodic Future Thinking as Digital Micro-interventions 25th

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Episodic Future Thinking as Digital Micro-interventions

25th International Conference on Human-computer Interaction, HCII 2023

作者： Persson, Dan Roland Yoo, Soojeong Bardram, Jakob E. Skinner, Timothy C. Bækgaard, Per Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark University College London Interaction Centre London United Kingdom Department of Health Technology Technical University of Denmark Kongens Lyngby Denmark Institute of Psychology University of Copenhagen Copenhagen Denmark

ISBN: (纸本)9783031480379

Micro-interventions are quick focused behavioural interventions aimed at matching users’ current capacity for engagement. Mobile devices are powerful, interactive, and sensor-rich platforms for delivering micro-interventions and for determining when and where to do so. This paper presents a novel smart-phone based approach to micro-interventions based on established ‘Episodic Future Thinking (EFT)’ research. The paper both presents the background for EFT-based micro-interventions and the design of an ‘EFT’ smartphone application implementing this. The approach and technology were evaluated in a feasibility study including 14 participants using the system for 14 days. Results demonstrate the feasibility of implementing EFT as micro-interventions, with participants willing to use the application, providing positive feedback and constructive suggestions. The paper concludes with a thorough discussion of the implications for smartphone-based EFT delivered as micro-interventions and how these can be used as part of a larger behaviour change and health improvement initiatives. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： mHealth

Preparing the Vuk’uzenzele and ZA-gov-multilingual South African multilingual corpora

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arXiv 2023年

作者： Lastrucci, Richard Dzingirai, Isheanesu Rajab, Jenalea Madodonga, Andani Shingange, Matimba Njini, Daniel Marivate, Vukosi Department of Computer Science University of Pretoria South Africa School of Computer Science and Applied Mathematics University of the Witwatersrand South Africa Lelapa AI South Africa

This paper introduces two multilingual government themed corpora in various South African languages. The corpora were collected by gathering the South African Government newspaper (Vuk’uzenzele), as well as South African government speeches (ZAgov-multilingual), that are translated into all 11 South African official languages. The corpora can be used for a myriad of downstream NLP tasks. The corpora were created to allow researchers to study the language used in South African government publications, with a focus on understanding how South African government officials communicate with their constituents. In this paper we highlight the process of gathering, cleaning and making available the corpora. We create parallel sentence corpora for Neural Machine Translation (NMT) tasks using Language-Agnostic Sentence Representations (LASER) embeddings. With these aligned sentences we then provide NMT benchmarks for 9 indigenous languages by fine-tuning a massively multilingual pre-trained language model. Copyright © 2023, The Authors. All rights reserved.

关键词： Computational linguistics

NETWORK INPAINTING VIA OPTIMAL TRANSPORT

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arXiv 2024年

作者： Facca, Enrico Nordbotten, Jan Martin Hanson, Erik Andreas Department of Mathematics University of Bergen Bergen Norway Department of Computer science Electrical engineering and Mathematical sciences Western Norway University of Applied Sciences Bergen Norway

In this work, we present a novel tool for reconstructing networks from corrupted images. The reconstructed network is the result of a minimization problem that has a misfit term with respect to the observed data, and a physics-based regularizing term coming from the theory of optimal transport. Through a range of numerical tests, we demonstrate that our suggested approach can effectively rebuild the primary features of damaged networks, even when artifacts are *** Codes 49-04, 49K20, 49N99, 65N21, 65N30, 65Z05 © 2024, CC BY.

关键词： Inverse problems